I want to install Oomph on my computer instead of starting installer exe file every time I want to install an Eclipse product. Is it possible? Previously I think it was possible... however with latest Oomph version I couldn't get it....

I downloaded the latest installer from https://wiki.eclipse.org/Eclipse_Installer and ran it. I used the menu to switch to Advanced Mode... and the popup dialog asks me if I want to keep the installer in a permanent location so that way certainly appears to work...